1. What is Mean Square?

Mean Square (MS) is a statistical measure that represents the average of squared deviations from the mean. It's calculated by dividing the sum of squares (SS) by the corresponding degrees of freedom (df).

2. How Does the Calculator Work?

The calculator uses the Mean Square formula:

Where:

• \( MS \) — Mean Square (units²)
• \( SS \) — Sum of Squares (units²)
• \( df \) — Degrees of Freedom

Explanation: The formula calculates the average squared deviation by accounting for the number of independent pieces of information.

3. Importance of Mean Square

Details: Mean Square is fundamental in ANOVA (Analysis of Variance) for comparing variances between groups and within groups. It helps determine if observed differences are statistically significant.

4. Using the Calculator

Tips: Enter the sum of squares (must be positive) and degrees of freedom (must be ≥1). The result will be in squared units of your original measurement.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between MS and variance?
A: Mean Square is essentially the same as variance - both measure average squared deviations. The term "mean square" is typically used in ANOVA contexts.

Q2: How do I calculate sum of squares?
A: SS = Σ(X - X̄)², where X is each observation and X̄ is the mean of all observations.

Q3: What are degrees of freedom?
A: df represents the number of independent pieces of information. For a sample, df = n - 1 where n is sample size.

Q4: When is mean square used?
A: Primarily in ANOVA for comparing group means and in regression analysis for assessing model fit.

Q5: Can mean square be negative?
A: No, since both SS and df are always positive, MS will always be positive or zero.